How to deform a plane according to the shape of other objects
If the base terrain plane is deformed by a displace modifier why not just give the second plane the same modifier stack?

If I understand correctly this is the effect you are aiming for, kind of like a manta-ray wavy hover motion



Just add a second plane above the first one, subdivide it accordingly, and link the modifiers to the original one. Select new plane > select terrain > Ctrl + L Modifiers.

Make sure both objects have the same displace modifier or most importantly share the same displace texture and with the both Texture Coordinates set to Global